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Copy pathoctonion.h
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octonion.h
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class octonion {
static int default_mult;
public:
double guts[8];
octonion () = delete;
octonion (octonion const &) = default;
octonion (octonion &&) = default;
octonion & operator= (octonion const &) = default;
octonion & operator= (octonion &&) = default;
~octonion () = default;
octonion (
double const e0, double const e1,
double const e2, double const e3,
double const e4, double const e5,
double const e6, double const e7
) {
guts[0] = e0; guts[1] = e1;
guts[2] = e2; guts[3] = e3;
guts[4] = e4; guts[5] = e5;
guts[6] = e6; guts[7] = e7;
}
octonion (double const (& g)[8]) {
for (int i {0}; i < 8; ++i) guts[i] = g[i];
}
octonion operator+ () const {
return octonion {
+guts[0], +guts[1], +guts[2], +guts[3],
+guts[4], +guts[5], +guts[6], +guts[7]
};
}
octonion operator~ () const {
return octonion {
+guts[0], -guts[1], -guts[2], -guts[3],
-guts[4], -guts[5], -guts[6], -guts[7]
};
}
octonion operator- () const {
return octonion {
-guts[0], -guts[1], -guts[2], -guts[3],
-guts[4], -guts[5], -guts[6], -guts[7]
};
}
octonion operator+ (octonion const & o) const {
return octonion {
guts[0] + o.guts[0], guts[1] + o.guts[1],
guts[2] + o.guts[2], guts[3] + o.guts[3],
guts[4] + o.guts[4], guts[5] + o.guts[5],
guts[6] + o.guts[6], guts[7] + o.guts[7]
};
}
octonion operator- (octonion const & o) const {
return octonion {
guts[0] - o.guts[0], guts[1] - o.guts[1],
guts[2] - o.guts[2], guts[3] - o.guts[3],
guts[4] - o.guts[4], guts[5] - o.guts[5],
guts[6] - o.guts[6], guts[7] - o.guts[7]
};
}
static void set_default_mult (int const choose_mult) {
if (choose_mult < 0)
throw fail {"octonion::set_default_mult ... choose_mult < 0"};
if (choose_mult > 479)
throw fail {"octonion::set_default_mult ... choose_mult > 479"};
default_mult = choose_mult;
}
static int get_default_mult () { return default_mult; }
octonion mult (octonion const & second, int const choose_mult) const {
if (choose_mult < 0)
throw fail {"octonion::mult ... choose_mult < 0"};
if (choose_mult > 479)
throw fail {"octonion::mult ... choose_mult > 479"};
int const (& source)[8][8] {raw_mult[choose_mult]};
octonion const & first {*this};
double r[8];
for (int i {0}; i < 8; ++i) r[i] = 0;
for (int i {0}; i < 8; ++i) {
for (int j {0}; j < 8; ++j) {
int const ij {source[i][j]};
if (ij == +8)
r[0] += first.guts[0] * second.guts[0];
else if (ij == -8)
r[0] -= first.guts[i] * second.guts[j];
else if (ij > 0)
r[+ij] += first.guts[i] * second.guts[j];
else if (ij < 0)
r[-ij] -= first.guts[i] * second.guts[j];
else
throw fail {"octonion::mult ... ij == 0"};
}
}
return octonion {r};
}
octonion operator* (octonion const & second) const {
return mult (second, default_mult);
}
octonion mult_aba (octonion const & second) const {
// Calculates (*this) * second * (*this).
// The value of default_mult does not matter.
double const (& t)[8] {this->guts};
double const (& s)[8] {second.guts};
double r[8];
double const t0 {t[0]};
double const s0 {s[0]};
r[0] = t0 * s0 * t0;
for (int i {1}; i < 8; ++i) {
double const ti {t[i]};
double const si {s[i]};
r[i] = -ti * si * ti;
r[0] -= t0 * si * ti;
r[0] -= ti * s0 * ti;
r[0] -= ti * si * t0;
r[i] += ti * s0 * t0;
r[i] += t0 * si * t0;
r[i] += t0 * s0 * ti;
for (int j {1}; j < 8; ++j) {
if (i == j) continue;
double const tj {t[j]};
double const sj {s[j]};
r[i] -= ti * sj * tj;
r[i] += tj * si * tj;
r[i] -= tj * sj * ti;
}
}
return octonion {r};
}
octonion mult_conj_aab (octonion const & second) const {
// calculates (~ *this) * (*this) * second
// the value of default_mult does not matter
double const (& t)[8] {this->guts};
double const (& s)[8] {second.guts};
double r[8];
double const t0 {t[0]};
double const s0 {s[0]};
r[0] = t0 * t0 * s0;
for (int i {1}; i < 8; ++i) {
double const ti {t[i]};
double const si {s[i]};
r[i] = +ti * ti * si;
r[0] -= t0 * ti * si;
r[0] += ti * t0 * si;
r[0] += ti * ti * s0;
r[i] -= ti * t0 * s0;
r[i] += t0 * ti * s0;
r[i] += t0 * t0 * si;
for (int j {1}; j < 8; ++j) {
if (i == j) continue;
double const tj {t[j]};
double const sj {s[j]};
r[i] += ti * tj * sj;
r[i] -= tj * ti * sj;
r[i] += tj * tj * si;
}
}
return octonion {r};
}
octonion operator* (double const o) const {
return octonion {
guts[0] * o, guts[1] * o, guts[2] * o, guts[3] * o,
guts[4] * o, guts[5] * o, guts[6] * o, guts[7] * o,
};
}
octonion operator/ (double const o) const {
return octonion {
guts[0] / o, guts[1] / o, guts[2] / o, guts[3] / o,
guts[4] / o, guts[5] / o, guts[6] / o, guts[7] / o,
};
}
double squ_abs () const {
double total {0.0};
for (int i {0}; i < 8; ++i)
total += guts[i] * guts[i];
return total;
}
double abs () const { return sqrt (squ_abs()); }
bool operator< (octonion const & o) const {
for (int i {0}; i < 8; ++i) {
if (guts[i] < o.guts[i]) return true;
if (guts[i] > o.guts[i]) return false;
}
return false;
}
octonion recip () const
{ return operator~() / squ_abs(); }
void view (ostream & o) const {
o << "[";
for (auto const i : guts) {
if (i > 0) {
o << std::showpos;
o << setw (12) << i << " ";
o << std::noshowpos;
} else {
o << setw (12) << i << " ";
}
}
o << "]";
}
};
int octonion::default_mult {42};
ostream & operator<< (ostream & ost, octonion const oct)
{ oct.view (ost); return ost; }